arXiv subjects

Eduardo Gildin

Publications and source records attributed to Eduardo Gildin.

16 recordsLinked to original sources

arXiv2025

Updating DMD Operators for Changes in Domain Properties

Fast and reliable surrogate models are critical for optimization, control and uncertainty analysis in geological carbon-storage projects, yet high-fidelity multiphase simulators remain too expensive. Dynamic Mode Decomposition (DMD) offers an attractive data-driven reduction framework, but its operators are trained for a single set of reservoir properties. When permeability or well location changes, conventional practice is to regenerate snapshots and retrain the surrogate, erasing most of the speed advantage. This work presents a lightweight alternative that updates an existing DMD or DMD-with-control model without incorporating new simulation data or retraining. Two complementary update strategies are introduced. For cases where permeability changes uniformly across the domain, the proposed updates adjust the models internal dynamics and control response to match the new flow timescale. When permeability varies in space, the approach modifies the spatial representation so that high-permeability zones are given greater influence on the models reduced basis. Numerical experiments demonstrate that the proposed updates recover plume migration and pressure build-up within three percent of a freshly trained surrogate yet execute hundreds of times faster than full retraining. These methods therefore enable real-time optimization and rapid what-if studies while preserving the physical fidelity demanded by carbon-storage workflows.

physics.comp-ph↗

arXiv2025

Introducing Coherent-Control Koopman Modeling to Reservoir Scale Porous Media Flow Studies

Accurate and robust surrogate modeling is essential for the real-time control and optimization of large-scale subsurface systems, such as geological CO2 storage and waterflood management. This study investigates the limits of classical Dynamic Mode Decomposition with control (DMDc) and introduces CCKM, as a robust alter-native, in enforcing control in pressure and water saturation reservoir dynamics under challenging prediction scenarios. We introduced a control-coherent incremental (Δ) CCKM formulation, in which the field update is driven by actuator changes rather than rather than actuator levels as in the original level formulation and compared them both against DMDc and a Hybrid B-only surrogate that re-uses DMDcs bottom-B (same-step feed-through), showing that only CCKM remains stable and accurate under regime shifts. Two representative cases are considered: (i) an out-of-distribution shut-in and restart case, and (ii) an in-distribution bottomhole pressure (BHP) drawdown. Results show that only CCKM consistently maintains stability and accuracy across both scenarios, achieving sub-bar mean absolute error and sub-percent Frobenius norm percent change error (FPCE) even under regime shifts, while DMDc exhibit large unphysical errors during control transients. The findings demonstrate that strict control-coherence is critical for reliable surrogate modeling, particularly in settings with abrupt changes in control strategy. The proposed framework is broadly applicable to real-time reservoir optimization and can be integrated seamlessly into existing optimization and monitoring workflows, enabling fast and trustworthy deci-sion support in the presence of both expected and unexpected actuation regimes.

eess.SY↗

arXiv2025

Deep Global Model Reduction Learning in Porous Media Flow Simulation

In this paper, we combine deep learning concepts and some proper orthogonal decomposition (POD) model reduction methods for predicting flow in heterogeneous porous media. Nonlinear flow dynamics is studied, where the dynamics is regarded as a multi-layer network. The solution at the current time step is regarded as a multi-layer network of the solution at the initial time and input parameters. As for input, we consider various sources, which include source terms (well rates), permeability fields, and initial conditions. We consider the flow dynamics, where the solution is known at some locations and the data is integrated to the flow dynamics by modifying the reduced-order model. This approach allows modifying the reduced-order formulation of the problem. Because of the small problem size, limited observed data can be handled. We consider enriching the observed data using the computational data in deep learning networks. The basis functions of the global reduced order model are selected such that the degrees of freedom represent the solution at observation points. This way, we can avoid learning basis functions, which can also be done using neural networks. We present numerical results, where we consider channelized permeability fields, where the network is constructed for various channel configurations. Our numerical results show that one can achieve a good approximation using forward feed maps based on multi-layer networks.

math.NA↗

arXiv2025

Data-driven models for production forecasting and decision supporting in petroleum reservoirs

Forecasting production reliably and anticipating changes in the behavior of rock-fluid systems are the main challenges in petroleum reservoir engineering. This project proposes to deal with this problem through a data-driven approach and using machine learning methods. The objective is to develop a methodology to forecast production parameters based on simple data as produced and injected volumes and, eventually, gauges located in wells, without depending on information from geological models, fluid properties or details of well completions and flow systems. Initially, we performed relevance analyses of the production and injection variables, as well as conditioning the data to suit the problem. As reservoir conditions change over time, concept drift is a priority concern and require special attention to those observation windows and the periodicity of retraining, which are also objects of study. For the production forecasts, we study supervised learning methods, such as those based on regressions and Neural Networks, to define the most suitable for our application in terms of performance and complexity. In a first step, we evaluate the methodology using synthetic data generated from the UNISIM III compositional simulation model. Next, we applied it to cases of real plays in the Brazilian pre-salt. The expected result is the design of a reliable predictor for reproducing reservoir dynamics, with rapid response, capability of dealing with practical difficulties such as restrictions in wells and processing units, and that can be used in actions to support reservoir management, including the anticipation of deleterious behaviors, optimization of production and injection parameters and the analysis of the effects of probabilistic events, aiming to maximize oil recovery.

cs.LG↗

arXiv2025

Identifying Large-Scale Linear Parameter Varying Systems with Dynamic Mode Decomposition Methods

Linear Parameter Varying (LPV) Systems are a well-established class of nonlinear systems with a rich theory for stability analysis, control, and analytical response finding, among other aspects. Although there are works on data-driven identification of such systems, the literature is quite scarce in terms of works that tackle the identification of LPV models for large-scale systems. Since large-scale systems are ubiquitous in practice, this work develops a methodology for the local and global identification of large-scale LPV systems based on nonintrusive reduced-order modeling. The developed method is coined as DMD-LPV for being inspired in the Dynamic Mode Decomposition (DMD). To validate the proposed identification method, we identify a system described by a discretized linear diffusion equation, with the diffusion gain defined by a polynomial over a parameter. The experiments show that the proposed method can easily identify a reduced-order LPV model of a given large-scale system without the need to perform identification in the full-order dimension, and with almost no performance decay over performing a reduction, given that the model structure is well-established.

eess.SY↗

arXiv2025

Dynamic Mode Decomposition Accelerated Forecast and Optimization of Geological CO2 Storage in Deep Saline Aquifers

Data-driven and non-intrusive DMDc and DMDspc models successfully expedite the reconstruction and forecasting of CO2 fluid flow with acceptable accuracy margins, aiding in the rapid optimization of geological CO2 storage forecast and optimization. DMDc and DMDspc models were trained with weekly, monthly, and yearly simulation pressure and CO2 saturation fields using a commercial simulator. The domain of interest is a large-scale, offshore, highly heterogeneous reservoir model with over 100,000 cells. DMD snapshot reconstruction significantly reduced simulation times from several hours to mere minutes. DMDspc reduced the number of DMD modes for pressure without losing accuracy while sometimes even improving accuracy. Two operation cases were considered: 1. CO2 injection, 2. CO2 injection and water production for pressure maintenance. For pressure, DMDspc achieved a slightly higher than DMDc average error by removing several modes. On the other hand, DMDspc showed limited success in reducing modes for CO2 saturation. The forecast performance of DMD models was evaluated using percent change error, mean absolute error and Pearsons R correlation coefficient metrics. Almost all DMD pressure models managed to successfully forecast pressure fields, while a smaller number of DMD models managed to forecast CO2 saturation. While forecast errors have a considerable range, only DMD models with errors below 5% PCE for pressure or 0.01 MAE for saturation were considered acceptable for geological CO2 storage optimization. Optimized CO2 injection and water production amounts were consistent across selected DMD models and all time scales. The DMDspc-monitored cells approach, which only reconstructs the monitored-during-optimization cells, reduced even further optimization time while providing consistent results with the optimization that used full snapshot reconstruction.

physics.comp-ph↗

arXiv2024

Multi-Step Embed to Control: A Novel Deep Learning-based Approach for Surrogate Modelling in Reservoir Simulation

Reduced-order models, also known as proxy model or surrogate model, are approximate models that are less computational expensive as opposed to fully descriptive models. With the integration of machine learning, these models have garnered increasing research interests recently. However, many existing reduced-order modeling methods, such as embed to control (E2C) and embed to control and observe (E2CO), fall short in long-term predictions due to the accumulation of prediction errors over time. This issue arises partly from the one-step prediction framework inherent in E2C and E2CO architectures. This paper introduces a deep learning-based surrogate model, referred as multi-step embed-to-control model, for the construction of proxy models with improved long-term prediction performance. Unlike E2C and E2CO, the proposed network considers multiple forward transitions in the latent space at a time using Koopman operator, allowing the model to incorporate a sequence of state snapshots during training phrases. Additionally, the loss function of this novel approach has been redesigned to accommodate these multiple transitions and to respect the underlying physical principles. To validate the efficacy of the proposed method, the developed framework was implemented within two-phase (oil and water) reservoir model under a waterflooding scheme. Comparative analysis demonstrate that the proposed model significantly outperforms the conventional E2C model in long-term simulation scenarios. Notably, there was a substantial reduction in temporal errors in the prediction of saturation profiles and a decent improvement in pressure forecasting accuracy.

cs.LG↗

arXiv2024

Physics-Informed Neural Networks for Multi-Phase Flow in Porous Media Considering Dual Shocks and Interphase Solubility

Physics-Informed Neural Networks (PINNs) integrate physical principles into machine learning, finding wide applications in various science and engineering fields. However, solving nonlinear hyperbolic partial differential equations (PDEs) with PINNs presents challenges due to inherent discontinuities in the solutions. This is particularly true for the Buckley-Leverett (B-L) equation, a key model for multi-phase fluid flow in porous media. In this paper, we demonstrate that PINNs, in conjunction with Welge's Construction, can achieve superior precision in handling the B-L equations in different scenarios including one shock and one rarefaction wave, two shocks connected by a rarefaction wave traveling in the same direction, and two shocks connected by a rarefaction wave traveling in opposite directions. Our approach accounts for variations in fluid mobility, fluid solubility, and gravity effects, with applications in modeling 1D water flooding, polymer flooding, gravitational flow, and CO$_2$ injection into saline aquifers. Additionally, we applied PINNs to inverse problems to estimate multiple PDE parameters from observed data, demonstrating robustness under conditions of slight scarcity and up to 5% impurity of labeled data, as well as shortages in collocation data.

physics.flu-dyn↗

arXiv2024

Neural Operator-Based Proxy for Reservoir Simulations Considering Varying Well Settings, Locations, and Permeability Fields

Simulating Darcy flows in porous media is fundamental to understand the future flow behavior of fluids in hydrocarbon and carbon storage reservoirs. Geological models of reservoirs are often associated with high uncertainly leading to many numerical simulations for history matching and production optimization. Machine learning models trained with simulation data can provide a faster alternative to traditional simulators. In this paper we present a single Fourier Neural Operator (FNO) surrogate that outperforms traditional reservoir simulators by the ability to predict pressures and saturations on varying permeability fields, well locations, well controls, and number of wells. The maximum-mean relative error of 95\% of pressure and saturation predictions is less than 5\%. This is achieved by employing a simple yet very effective data augmentation technique that reduces the dataset size by 75\% and reduces overfitting. Also, constructing the input tensor in a binary fashion enables predictions on unseen well locations, well controls, and number of wells. Such model can accelerate history matching and reservoir characterization procedures by several orders of magnitude. The ability to predict on new well locations, well controls, and number of wells enables highly efficient reservoir management and optimization.

physics.flu-dyn↗

arXiv2024

Optimization of Pressure Management Strategies for Geological CO2 Sequestration Using Surrogate Model-based Reinforcement Learning

Injecting greenhouse gas into deep underground reservoirs for permanent storage can inadvertently lead to fault reactivation, caprock fracturing and greenhouse gas leakage when the injection-induced stress exceeds the critical threshold. Extraction of pre-existing fluids at various stages of injection process, referred as pressure management, can mitigate associated risks and lessen environmental impact. However, identifying optimal pressure management strategies typically requires thousands of full-order simulations due to the need for function evaluations, making the process computationally prohibitive. This paper introduces a novel surrogate model-based reinforcement learning method for devising optimal pressure management strategies for geological CO2 sequestration efficiently. Our approach comprises two steps. Firstly, a surrogate model is developed through the embed to control method, which employs an encoder-transition-decoder structure to learn latent dynamics. Leveraging this proxy model, reinforcement learning is utilized to find an optimal strategy that maximizes economic benefits while satisfying various control constraints. The reinforcement learning agent receives the latent state space representation and immediate reward tailored for CO2 sequestration and choose real-time controls which are subject to predefined engineering constraints in order to maximize the long-term cumulative rewards. To demonstrate its effectiveness, this framework is applied to a compositional simulation model where CO2 is injected into saline aquifer. The results reveal that our surrogate model-based reinforcement learning approach significantly optimizes CO2 sequestration strategies, leading to notable economic gains compared to baseline scenarios.

cs.CE↗

arXiv2023

Physics-Informed Neural Network for the Transient Diffusivity Equation in Reservoir Engineering

Physics-Informed machine learning models have recently emerged with some interesting and unique features that can be applied to reservoir engineering. In particular, physics-informed neural networks (PINN) leverage the fact that neural networks are a type of universal function approximators that can embed the knowledge of any physical laws that govern a given data-set in the learning process, and can be described by partial differential equations. The transient diffusivity equation is a fundamental equation in reservoir engineering and the general solution to this equation forms the basis for Pressure Transient Analysis (PTA). The diffusivity equation is derived by combining three physical principles, the continuity equation, Darcy's equation, and the equation of state for a slightly compressible liquid. Obtaining general solutions to this equation is imperative to understand flow regimes in porous media. Analytical solutions of the transient diffusivity equation are usually hard to obtain due to the stiff nature of the equation caused by the steep gradients of the pressure near the well. In this work we apply physics-informed neural networks to the one and two dimensional diffusivity equation and demonstrate that decomposing the space domain into very few subdomains can overcome the stiffness problem of the equation. Additionally, we demonstrate that the inverse capabilities of PINNs can estimate missing physics such as permeability and distance from sealing boundary similar to buildup tests without shutting in the well.

physics.flu-dyn↗

arXiv2023

Transfer learning-based physics-informed convolutional neural network for simulating flow in porous media with time-varying controls

A physics-informed convolutional neural network is proposed to simulate two phase flow in porous media with time-varying well controls. While most of PICNNs in existing literatures worked on parameter-to-state mapping, our proposed network parameterizes the solution with time-varying controls to establish a control-to-state regression. Firstly, finite volume scheme is adopted to discretize flow equations and formulate loss function that respects mass conservation laws. Neumann boundary conditions are seamlessly incorporated into the semi-discretized equations so no additional loss term is needed. The network architecture comprises two parallel U-Net structures, with network inputs being well controls and outputs being the system states. To capture the time-dependent relationship between inputs and outputs, the network is well designed to mimic discretized state space equations. We train the network progressively for every timestep, enabling it to simultaneously predict oil pressure and water saturation at each timestep. After training the network for one timestep, we leverage transfer learning techniques to expedite the training process for subsequent timestep. The proposed model is used to simulate oil-water porous flow scenarios with varying reservoir gridblocks and aspects including computation efficiency and accuracy are compared against corresponding numerical approaches. The results underscore the potential of PICNN in effectively simulating systems with numerous grid blocks, as computation time does not scale with model dimensionality. We assess the temporal error using 10 different testing controls with variation in magnitude and another 10 with higher alternation frequency with proposed control-to-state architecture. Our observations suggest the need for a more robust and reliable model when dealing with controls that exhibit significant variations in magnitude or frequency.

cs.LG↗

arXiv2023

Investigation of Proper Orthogonal Decomposition for Echo State Networks

Echo State Networks (ESN) are a type of Recurrent Neural Network that yields promising results in representing time series and nonlinear dynamic systems. Although they are equipped with a very efficient training procedure, Reservoir Computing strategies, such as the ESN, require high-order networks, i.e., many neurons, resulting in a large number of states that are magnitudes higher than the number of model inputs and outputs. A large number of states not only makes the time-step computation more costly but also may pose robustness issues, especially when applying ESNs to problems such as Model Predictive Control (MPC) and other optimal control problems. One way to circumvent this complexity issue is through Model Order Reduction strategies such as the Proper Orthogonal Decomposition (POD) and its variants (POD-DEIM), whereby we find an equivalent lower order representation to an already trained high dimension ESN. To this end, this work aims to investigate and analyze the performance of POD methods in Echo State Networks, evaluating their effectiveness through the Memory Capacity (MC) of the POD-reduced network compared to the original (full-order) ESN. We also perform experiments on two numerical case studies: a NARMA10 difference equation and an oil platform containing two wells and one riser. The results show that there is little loss of performance comparing the original ESN to a POD-reduced counterpart and that the performance of a POD-reduced ESN tends to be superior to a normal ESN of the same size. Also, the POD-reduced network achieves speedups of around $80\%$ compared to the original ESN.

cs.LG↗

arXiv2023

Physics-informed Convolutional Recurrent Surrogate Model for Reservoir Simulation with Well Controls

This paper presents a novel surrogate model for modeling subsurface fluid flow with well controls using a physics-informed convolutional recurrent neural network (PICRNN). The model uses a convolutional long-short term memory (ConvLSTM) to capture the spatiotemporal dependencies of the state evolution dynamics in the porous flow. The ConvLSTM is linked to the state space equations, enabling the incorporation of a discrete-time sequence of well control. The model requires initial state condition and a sequence of well controls as inputs, and predicts the state variables of the system, such as pressure, as output. By minimizing the residuals of reservoir flow state-space equations, the network is trained without the need for labeled data. The model is designed to serve as a surrogate model for predicting future reservoir states based on the initial reservoir state and input engineering controls. Boundary conditions are enforced into the state-space equations so no additional loss term is needed. Three numerical cases are studied, demonstrating the model's effectiveness in predicting reservoir dynamics based on future well/system controls. The proposed model provides a new approach for efficient and accurate prediction of subsurface fluid flow, with potential applications in optimal control design for reservoir engineering.

cs.LG↗

arXiv2021

DREAMS: Drilling and Extraction Automated System

Drilling and Extraction Automated System (DREAMS) is a fully automated prototype-drilling rig that can drill, extract water and assess subsurface density profiles from simulated lunar and Martian subsurface ice. DREAMS system is developed by the Texas A&M drilling automation team and composed of four main components: 1- tensegrity rig structure, 2- drilling system, 3- water extracting and heating system, and 4- electronic hardware, controls, and machine algorithm. The vertical and rotational movements are controlled by using an Acme rod, stepper, and rotary motor. DREAMS is a unique system and different from other systems presented before in the NASA Rascal-Al competition because 1- It uses the tensegrity structure concept to decrease the system weight, improve mobility, and easier installation in space. 2- It cuts rock layers by using a short bit length connected to drill pipes. This drilling methodology is expected to drill hundreds and thousands of meters below the moon and Martian surfaces without any anticipated problems (not only 1 m.). 3- Drilling, heating, and extraction systems are integrated into one system that can work simultaneously or individually to save time and cost.

cs.RO↗

arXiv2020

Non-Intrusive Parametric Model Order Reduction With Error Correction Modeling for Changing Well Locations Using a Machine Learning Framework

The objective of this paper is to develop a global non-intrusive Parametric Model Order Reduction (PMOR) methodology for the problem of changing well locations in an oil field, that can eventually be used for well placement optimization to gain significant computational savings. In this work, we propose a proper orthogonal decomposition (POD) based PMOR strategy that is non-intrusive to the simulator source code and hence extends its applicability to any commercial simulator. The non-intrusiveness of the proposed technique stems from formulating a novel Machine Learning (ML) based framework used with POD. The features of ML model are designed such that they take into consideration the temporal evolution of the state solutions and thereby avoiding simulator access for time dependency of the solutions. We represent well location changes as a parameter by introducing geometry-based features and flow diagnostics inspired physics-based features. An error correction model based on reduced model solutions is formulated later to correct for discrepancies in the state solutions at well gridblocks. It was observed that the global PMOR could predict the overall trend in pressure and saturation solutions at the well blocks but some bias was observed that resulted in discrepancies in prediction of quantities of interest (QoI). Thus, the error correction model that considers the physics based reduced model solutions as features, proved to reduce the error in QoI significantly. This workflow is applied to a heterogeneous channelized reservoir that showed good solution accuracies and speed-ups of 50x-100x were observed for different cases considered. The method is formulated such that all the simulation time steps are independent and hence can make use of parallel resources very efficiently and also avoid stability issues that can result from error accumulation over timesteps.

cs.CE↗